ISTANBUL—Turkey pushed back against fresh criticism of its efforts to control the movement of extremists through its territory, as the government disclosed that the partner of one of the Paris attackers crossed the Turkish border into Syria during last week’s terror spree.

Turkey’s foreign ministry said Hayat Boumeddiene, who is wanted by French authorities, entered Syria on Thursday, the day her partner, Amedy Coulibaly, killed a policewoman on Paris’s outskirts and a day after the mass shooting at the magazine Charlie...